How can I control the length of hair particles
Create a plane
Add particles and select Hair (as you've already done)
Style you hair see the following GIF

Now from Modifiers hit Convert


This will convert hair into a mesh

Now keep whatever you want, and delete whatever you don't need.

EDITED: To make it a little more controlled.. 

In these steps I gave thickness to "only-edges-mesh", because Hair by default are paths. converted into mesh by applying the modifier.


in this images.. I changed into "editable mode"
then selected "Edge" type (not vertex or face).
move to very close to the edge.
pressed "A" to select all edges (hair)
pressed "E" for extrude and pressed "x" to extruded the edge into "X" direction
pressed "A" again to select all edges 
Pressed "E" to extrude and pressed "Y" to lock extrude only into "Y" direction.
.. see these are no cubic hair.
Added a box to boolean hair with it. 



in this image..I am modifying with "Boolean"


scaled up the newly added box
positioned the box
selected hair.. and applied "Boolean" Modifier.
changed the boolean type..
changed the view to wireframe so I could see .. what is going on.
scaled up the box to the desired form..
Apply this modifier and that's what you needed.. right?